{
  "abstract": "Sections 2--3 of this note were prepared primarily for the author's private use, as a means of organizing the materials in (generally non-holomorphic) conformal field theory (CFT) on 2-dimensions in the language of the vertex operator algebra, and also of collecting subtle details. The choice of topics is intended to supplement introductory physics textbooks on the subject. Section 4 deals with (generally non-holomorphic) Type 0 CFTs in the language of vertex operator superalgebra (SVOA). Formulations of crossing symmetry and intertwining superoperators [resp. CFT vertex superoperators] of states in the Ramond (SVOA-twisted) sector [resp. the Ramond--Ramond sector] are presented by using two auxiliary parameters. The formulation allows systematic generalization to the class of simple current extensions characterized by four conditions: (1) the vanishing third cohomology, (2) skew-symmetric bimultiplicative form, (3) fixed-point-free action of simple currents, and (4) one additional condition described in the main text.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03725",
  "author_total": 1,
  "authors": [
    {
      "name": "Taizan Watari"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b4p72s3ttb4qm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03725",
  "fulltext_url": null,
  "id": "b4p72s3ttb4qm",
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  "landing_url": "https://arxiv.org/abs/2610.03725",
  "language": null,
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  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7220681105",
  "pdf_url": "https://arxiv.org/pdf/2610.03725",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b4p72s3ttb4qm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2610.03725",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03725"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Supplementary Notes on VOA and 2D SCFT",
  "title_text": "Supplementary Notes on VOA and 2D SCFT",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/b4p72s3ttb4qm",
  "venue": "arXiv",
  "versions": []
}